All complete intersection Calabi-Yau four-folds

Abstract

We present an exhaustive, constructive, classification of the Calabi-Yau fourfolds which can be described as complete intersections in products of projective spaces. A comprehensive list of 921,497 configuration matrices which represent all topologically distinct types of complete intersection Calabi-Yau four-folds is provided and can be downloaded here. The manifolds have non-negative Euler characteristics in the range 0 ≤ χ ≤ 2610. This data set will be of use in a wide range of physical and mathematical applications. Nearly all of these four-folds are elliptically fibered and are thus of interest for F-theory model building.

Jumping spectra and vanishing couplings in heterotic Line Bundle Standard Models

“…We will consider a particular existent Line Bundle Standard Model data set [19,20] built over Calabi-Yau manifolds which can be described as quotients of complete intersections in products of projective spaces (CICYs) [70][71][72][73][74][75][76]. Note that analogous constructions could be pursued over different base spaces, such as quotients of gCICYs [77] or toric hypersurfaces [78][79][80][81][82].…”

On the prevalence of elliptic and genus one fibrations among toric hypersurface Calabi-Yau threefolds

“…In a companion paper to this one [23], we use this approach to show that all Hodge numbers with h 1,1 or h 2,1 greater or equal to 240 that arise in the Kreuzer-Skarke database are realized explicitly by elliptic fibration constructions over toric or related base surfaces. Finally, from a somewhat different point of view the analysis of complete intersection Calabi-Yau manifolds and generalizations thereof has shown that these classes of Calabi-Yau threefolds and fourfolds are also overwhelmingly dominated by elliptic and genus one fibrations [24][25][26][27][28][29].…”

Getting CICY high

“…The CICY fourfolds are catalogued in [47]. (There are 921 497 configuration matrices most of which correspond to elliptically fibered Calabi-Yau spaces.)…”